Fixed Points of Generalized Pseudo-Contractions: Existence and Stability

We present an extension of Nadler's fixed point theorem and its local version for a class of multivalued maps that contains the pseudo-contractions. Relatively to a modulus, we propose conditions to ensure existence of fixed points with a quantitative estimate (depending on the modulus) about the distance of a reference point to the fixed point set. Some stability properties are established and are applied to the study of convergence of fixed point sets.